# Factors and Multiples

Factors and multiples are different things.

But they both involve multiplication:

• Factors are what we can multiply to get the number
• Multiples are what we get after multiplying the number by an integer (not a fraction).

### Example: the positive factors, and some multiples, of 6: Factors:

• 1 × 6 = 6, so 1 and 6 are factors of 6
• 2 × 3 = 6, so 2 and 3 are factors of 6

Multiples:

• 0 × 6 = 0, so 0 is a multiple of 6
• 1 × 6 = 6, so 6 is a multiple of 6
• 2 × 6 = 12, so 12 is a multiple of 6
• and so on

(Note: there are negative factors and multiples as well)

Here are the details:

## Factors

"Factors" are the numbers we can multiply together to get another number: 2 and 3 are factors of 6

A number can have many factors.

### Example: 12

• 3 × 4 = 12, so 3 and 4 are factors of 12
• Also 2 × 6 = 12, so 2 and 6 are also factors of 12,
• And 1 × 12 = 12, so 1 and 12 are factors of 12 as well.

AND because multiplying negatives makes a positive, −1, −2, −3, −4, −6 and −12 are also factors of 12:

• (−1) × (−12) = 12
• (−2) × (−6) = 12
• (−3) × (−4) = 12

So ALL the factors of 12 are:

1, 2, 3, 4, 6 and 12
AND −1, −2, −3, −4, −6 and −12

Learn about Greatest Common Factor and how to find All Factors of a Number.

## Multiples

A multiple is the result of multiplying a number by an integer (not a fraction).

### Example: Multiples of 3: ..., −9, −6, −3, 0, 3, 6, 9, ...

Example: 15 is a multiple of 3, as 3 × 5 = 15
Example: 16 is not a multiple of 3

### Example: Multiples of 5: ..., −15, −10, −5, 0, 5, 10, 15, ...

Example: 10 is a multiple of 5, as 5 × 2 = 10
Example: 11 is not a multiple of 5